Environmental uncertainties present significant challenges to sustainable supply chain management (SSCM), and often result in elevated costs, unsustainable production practices, and operational disruptions. In this study, we present a novel sustainable supply chain model with multiple objectives, utilizing the Golden Eagle Algorithm (GEA) for optimization. The model simultaneously addressed economic, environmental, and operational objectives, which included production, transportation, inventory management, shortages, recycling, and pollution mitigation. To manage the inherent complexity and uncertainty of decision variables, a descriptive-analytical research methodology was employed. Given the large-scale, NP-hard nature of the problem, exact solution methods, or commercial optimization software, such as GAMS and Simplex, proved infeasible. The GEA was implemented with parameters calibrated via the Taguchi method (Max Iterations = 23, Population Size = 40, Attack Propensity = 1.7–2, Cruise Propensity = 0.5–1). Ten randomly generated problem instances were used to rigorously evaluate algorithmic performance. Algorithm performance was assessed using multiple metrics, including MID (convergence), DM, NPS, and SNS (diversity and spread). Our results demonstrated that the GEA effectively explored the solution space, avoids local optima, and produces high-quality solutions. In smaller-scale problems (Example 8), the algorithm exhibited superior computational efficiency, whereas in larger-scale instances (Example 10), it achieved enhanced solution diversity (high DM) alongside effective convergence. These findings indicated that the model is feasible, robust, and practically applicable, and provides supply chain managers with a trustworthy tool to support their decision-making. Furthermore, the model's efficiency was demonstrated through numerical calculations.
Citation: Massoumeh Nazari. Optimization of a bi-objective sustainable supply chain model under uncertainty based on the Internet of Things[J]. Journal of Industrial and Management Optimization, 2026, 22(3): 1519-1538. doi: 10.3934/jimo.2026056
Environmental uncertainties present significant challenges to sustainable supply chain management (SSCM), and often result in elevated costs, unsustainable production practices, and operational disruptions. In this study, we present a novel sustainable supply chain model with multiple objectives, utilizing the Golden Eagle Algorithm (GEA) for optimization. The model simultaneously addressed economic, environmental, and operational objectives, which included production, transportation, inventory management, shortages, recycling, and pollution mitigation. To manage the inherent complexity and uncertainty of decision variables, a descriptive-analytical research methodology was employed. Given the large-scale, NP-hard nature of the problem, exact solution methods, or commercial optimization software, such as GAMS and Simplex, proved infeasible. The GEA was implemented with parameters calibrated via the Taguchi method (Max Iterations = 23, Population Size = 40, Attack Propensity = 1.7–2, Cruise Propensity = 0.5–1). Ten randomly generated problem instances were used to rigorously evaluate algorithmic performance. Algorithm performance was assessed using multiple metrics, including MID (convergence), DM, NPS, and SNS (diversity and spread). Our results demonstrated that the GEA effectively explored the solution space, avoids local optima, and produces high-quality solutions. In smaller-scale problems (Example 8), the algorithm exhibited superior computational efficiency, whereas in larger-scale instances (Example 10), it achieved enhanced solution diversity (high DM) alongside effective convergence. These findings indicated that the model is feasible, robust, and practically applicable, and provides supply chain managers with a trustworthy tool to support their decision-making. Furthermore, the model's efficiency was demonstrated through numerical calculations.
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Massoumeh Nazari. Optimization of a bi-objective sustainable supply chain model under uncertainty based on the Internet of Things[J]. Journal of Industrial and Management Optimization, 2026, 22(3): 1519-1538. doi: 10.3934/jimo.2026056
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